"His development is better than expected", trainer Fabio Mahseredjian told journalists.
'We will try to speed up his adaptation so he picks up his game pace'.
Brazil national team doctor Rodrigo Lasmar has said the former Santos prodigy is on track to be in peak condition for Brazil's first World Cup match against Switzerland on June 17.
Neymar is arguably Brazil's most important player, and the five-time World Cup winners will need him at his best if they are to add a sixth trophy to their cabinet.
Costa picked up the injury during Juventus' 2-1 win against Verona last weekend and is not expected to start training with his team-mates until the end of the week.
The Brazilian strikes a football comfortably
Neymar will have a chance to get back to match fitness with a friendly against Croatia on June 3 and Austria on June 10.
"He is being followed day by day so he can be cleared (to go to training)", Lasmar said.
The squad have gathered at Granja Comary, in a training centre in Teresopolis to begin their build-up for the summer.
They stormed through the notoriously hard South American qualifiers, and have been put in a group with Costa Rica, Switzerland and Serbia.
NFL to issue fines for kneeling during the national anthem
On Tuesday, it was reported that the league would assess 15-yard penalties to teams whose players protested on the sidelines. The new rule will be included in the NFL's game operations manual, which means it is not subject to collective bargaining.